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Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = e - 1, s = r/(1-r).
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%I #6 Dec 21 2016 10:48:19

%S 2,-2,3,-2,-2,8,-14,17,-12,-5,34,-68,91,-80,11,126,-308,467,-488,235,

%T 382,-1316,2291,-2760,1995,638,-5220,10738,-14725,13447,-3007,-18467,

%U 47914,-74806,80821,-43890,-51936,201548,-363193,450980,-347117,-55972,782359

%N Coefficients in the expansion of ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = e - 1, s = r/(1-r).

%H Clark Kimberling, <a href="/A279632/b279632.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: ([s] + [2s]x + [3s]x^2 + ...)/([r] + [2r]x + [3r]x^2 + ...); [ ] = floor, r = sqrt(2), s = r/(1-r).

%t z = 100;

%t r = E - 1; f[x_] := f[x] = Sum[Floor[r*(k + 1)] x^k, {k, 0, z}];

%t s = r/(r - 1); g[x_] := g[x] = Sum[Floor[s*(k + 1)] x^k, {k, 0, z}]

%t CoefficientList[Series[g[x]/f[x], {x, 0, z}], x]

%Y Cf. A000210, A054385.

%K sign,easy

%O 0,1

%A _Clark Kimberling_, Dec 18 2016